Uniqueness of static decompositions (Q620449)

The paper classifies static manifolds which admit more than one static decomposition whenever a condition on the curvature is fulfilled. For this, the authors take a standard static vector field and analyze its associated one parameter family of projections onto the base. A mild curvature hypothesis about the base or Einstein assumption is used. It is shown that in the Lorentzian case the uniqueness is guaranteed if the light-like sectional curvature at a point is never zero.